Received: 4 January 2023 Revised: 28 February 2023 Accepted: 4 April 2023 IET Renewable Power Generation

DOI: 10.1049/rpg2.12739

ORIGINAL RESEARCH

Artificial neural network assisted robust droop control

of autonomous microgrid

Sidra Kanwal1 Muhammad Qasim Rauf2 Bilal Khan1 Geev Mokryani3

1
Department of Electrical and Computer Abstract
Engineering, COMSATS University Islamabad,
Electric grid is vulnerable to power imbalance and inertia is the grid’s response to overcome
Abbottabad Campus, Abbottabad, KPK, Pakistan
2
such disturbance. Augmentation of power electronic converter based renewable energy
Department of Electrical Engineering, Capital
University of Science and Technology, Islamabad,
technologies like Photovoltaic Generators (PVG) and batteries in utility grid significantly
Pakistan reduces inertia. Inertia degradation is indicated by sharp Rate of Change of Frequency
3
Faculty of Engineering on Informatics, University (ROCOF) events due to any grid component failure or imbalance. Fixed gain feedback
of Bradford, Bradford, United Kingdom Proportional Integral Derivative (PID) control is insufficient to deal with varying ROCOF
events. This work proposes Sliding Mode (SM) robust droop control scheme assisted by
Correspondence Artificial Neural Network (ANN) algorithm for an islanded PVG integrated microgrid.
Geev Mokryani, Faculty of Engineering on
Informatics, University of Bradford BD7 1DP,
Droop response is governed by swing equation that uses PVG Maximum Power Point
UK.Email: g.mokryani@bradford.ac.uk (MPP) forecasted by ANN. ANN forecast is compared with optimized Gaussian process
regression algorithm based on mean squared error and speed of training as key perfor-
Funding information mance indicator. The algorithms are trained and validated based on climate dataset of
Innovate UK GCRF Energy Catalyst Pi-CREST
Islamabad, Pakistan. SM control performance is compared with various PID gain settings
project, Grant/Award Number: 41358; British
Academy GCRF COMPENSE project, and qualified as the most suitable against variable source, load and ROCOF scenarios.
Grant/Award Number: GCRFNGR3∖1541 Finally, significance of accurate MPP forecast for droop control is established by com-
paring the ANN and deterministic forecaster assisted droop response in a microgrid case
study.

1 INTRODUCTION ability to reject such disturbances. Cumulative grid inertia drops

with the entry of power electronic converter-based REs like
Global warming is expected to significantly impact international Photovoltaic Generators (PVG), fuel cells and batteries [6]. The
economy, food security, biodiversity, and potentially trigger significant challenge posed by low inertia is high Rate of Change
international conflicts. Signatory nations of 2015 Paris accord of Frequency (ROCOF) that can be observed during sudden
pledged to keep global temperature below 2◦ C that of pre- grid anomalies of fault, connection or disconnection of large
industrial levels [1, 2]. Energy sector renaissance is envisioned power source or load etc. [7]. According to [8], all the power
in [1] to systematically reduce fossil-fuel reliance and pro- generating modules including Demand Response (DR) services,
mote renewable energy (RE) alternatives. According to United HVDC systems, and microgrids must resume operation and
Nations Department of Economic and Social Affairs, Pakistan attempt to restore grid under ROCOF as high as 4 Hz/s. Failure
is the fifth most populous country in the world [3]. Pakistan has to address ROCOF problem trips protective relays, stresses
taken a number of initiatives to launch renewable energy power mechanical grid components and in worst case leads to cas-
projects and reduce the impact of imported fossil fuels on caded blackouts. Therefore, there is a substantial motivation to
electricity generation []. Photovoltaic (PV) energy is the prime research on ROCOF response improvement of power systems
contributor in these projects, accounting for approximately with low inertia exists. Rapid insertion or removal of grid power
400MW of electricity generation [4]. solves high ROCOF problem [9]. Recently, numerous studies
Utility grid stability is vulnerable due to disturbances in elec- have examined impact on electric grid stability by replacing con-
tric power demand and supply [5] and inertia is the inherent grid ventional generators with PVGs. Inertia is stored in the rotating

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is
properly cited.
© 2023 The Authors. IET Renewable Power Generation published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.

IET Renew. Power Gener. 2023;1–24. wileyonlinelibrary.com/iet-rpg 1

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2 KANWAL ET AL.

mass of synchronous generator and it enables grid frequency alternative to PI for better performance [30]. Robust con-
support. Frequency support is controlled by grid operator trol system aided by Artificial Intelligence (AI) to map system
that controls active power insertion or removal from grid [10]. dynamics is promising research frontier. AI is expected to
Inaccurate and sluggish deployment of frequency support significantly bridge the gap between complexity of robust con-
creates frequency deviations outside the acceptable range. The trol systems like Model Predictive Control (MPC) in [31] and
acceptable range or frequency dead band in Pakistan is ±1% of performance. Recent studies include Machine Learning (ML)
nominal frequency of 50 Hz [11]. Energy markets sought rapid based virtual inertia emulation for PVG based synchronverter
frequency regulation, and grid operator delivers such rapid [30] and fuzzy logic-based controller for microgrid voltage and
response by tightening governor frequency dead-bands. Gover- frequency regulation [32]. ANN based droop control law devel-
nors are responsible for primary frequency response. Tightening oped to control power electronic converters in [33] is used
governor dead-bands results in wear and tear in rotating equip- to dispatch an islanded DC microgrid. Hardware in the Loop
ment of synchronous generator, resulting in inefficient machine (HIL) verification of ANN based dynamic power management
operation [10, 12]. strategy for a DC microgrid is reported in [34]. Performance
The detailed nonlinear mathematical model based on swing recovery controller proposed in [35] used finite state machine
equation is presented in [13] that emulates inertia for power architecture and droop control to perform voltage regulation
electronic converters. Swing equation is used to incorporate and accurate current sharing in a DC microgrid. DC micro-
inertia, damping and frequency active power-based droop char- grid mandates a constant DC link voltage, and the study in
acteristics in grid interfaced converters [14]. A weak grid with [36] used ANN to regulate power sharing between two elec-
poor inertial response can be aided by proper energy storage trical sources with controlled ripple content. Study in [37]
systems [15]. Autonomous or islanded microgrids can bet- employed Yellow Saddle Goatfish algorithm to optimally tune
ter respond to sudden grid power imbalance events through parameters of a dual-stage fractional order PID controller, and
ultrashort term power injections using modern Energy Storage evaluated controller response against ROCOF, line-power fluc-
Systems (ESS) [16–18]. Fast and accurate power and frequency tuation and objective function. Hierarchical control systems
droop response of two PVGs is described [9]. Output power [38–40] used Radial Function based Neural Network to assist
is adaptively modulated by controlling PVG output voltage, in droop response. However, aforementioned strategies exhib-
controlled in response to programmable ROCOF events. Pri- ited sluggish response due to several control layers. Sliding
mary frequency response using smart loads of motor drives Mode (SM) control is single layer control and described sig-
and electric springs for British electric grid is illustrated in nificant transient and stability response for islanded microgrids
[19]. Active Power Control (APC) using PVGs is faster than [41, 42]. However, SM control is inherently plagued by chat-
governor speed control of synchronous machine. However, tering issues during sliding phase. ANN is used to resolve
frequency response of APC is sluggish in comparison with gain retuning problem using Lyapunov analysis [43]. Study
inertial response of synchronous machine [9]. Classical PVG in [44] used Takagi-Sugeno (TS) fuzzy inference control to
controllers are designed to extract maximum efficiency. and regulate load voltage and enable power sharing among micro-
consequently, PVGs inherently lack power reserve inertia for grid components. However, implementation of such systems is
frequency support. One alternative to emulate inertia in PVG problematic due to level of complexity associated with fuzzy
is to operate them at a derated power level [20, 5, 21]. Der- controllers [45].
ated PVG operation eliminates the need of expensive ESS and In order to establish the importance of an accurate inertia
is proven economically more feasible [22], primarily due to dra- estimation ML algorithm for a PVG and the design of robust
matic decline in PVG component cost than batteries [23]. The droop control mechanism, this paper presents a nonlinear SM
study in [24] emulated inertia by controlling DC link voltage control law aided by ANN to solve a swing equation. Estima-
and produced derated PVG power. Linear Quadratic Regula- tion results from ANN, GPR and deterministic techniques for
tor (LQR) is used to obtain optimum control trajectory and a 350 kW PVG are compared using mainstream ML workflow.
enhance grid inertia as reported in [25]. Virtual inertia of a ML algorithm is trained using climate data obtained from a tier-
Doubly Fed Induction Generator (DFIG) is augmented by 1 weather station installed at Islamabad campus of National
Lithium-ion supercapacitors on DC bus [26]. Studies in [27, University of Science and Technology. Climate data is consisted
28] have suggested to store inertia as electrostatic energy in on Global Horizontal Irradiance (GHI) and Dry Bulb Temper-
capacitors connected on DC bus of High Voltage DC (HVDC) ature (DBT) from CMP21 pyranometer and CS215 temperature
networks. Study in [29] devised novel grid frequency estimation probe, respectively [46].
technique instead of classical PLL based frequency calculator, The key contributions of this study are:
and injected active power into microgrid using proportional
control. ∙ MPP of PVG is estimated using accurate ML based fore-
Maximum efficiency extraction from PVG requires hill- caster, and is used to predict the instantaneous maximum
climbing control operation around nonlinear Power vs. Voltage power of PVG using the swing equation. ANN and Gaussian
characteristic curve of that PVG. Classically, feedback Pro- Process Regression (GPR) are trained and fine-tuned using
portional Integral (PI) controller is used to control linearized historical climate data of Islamabad, Pakistan. The two algo-
PVG. However, changing operational dynamics demand robust rithms are compared with deterministic forecaster, and Mean
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KANWAL ET AL. 3

Squared Error (MSE) is used as a key performance indica- Ideally the load current IL is related to the output voltage VL
tor. ANN is qualified as the most accurate algorithm with by Kirchhoff Current Law [22]:
minimum training time and validation MSE.
( )
∙ Robust Sliding Mode (SM) controller based on pulse-width VL +IL RS
−1 VL + IL RS
modulation is designed with constant frequency of oper- IL = IPH − ISat e nVT
− (2)
RSH
ation. The outcome of constant frequency operation is
near zero steady state voltage and power error. SM droop
Nevertheless, (2) is highly non-linear and internal parameters
controller for PVG is qualified against static and dynamic
like RS and RSH are not directly measurable. The reason is that
ROCOF events. SM droop response is compared with
these parameters are dependent on climate conditions of GHI
fixed gain PID controllers and former exhibited excellent
and DBT. Consequently, IL is not directly available to solve (1).
error performance under varying source, load and ROCOF
Numerous techniques are available in literature to linearize (2),
conditions.
such as GPR [22], genetic algorithm [47], pattern search opti-
∙ Importance of accurate PVG inertia estimation is highlighted
mization [48], particle swarm optimization [49], semi-analytic
in the context of aforementioned ROCOF events. ANN
method [50], semi-pattern search optimization [51], and Lam-
forecast is compared with GPR and deterministic linearized
bert W function [52]. Performing DC sweep analysis on VL
physical model of PVG. Deterministic model returned higher
between [0, VOC ] as done in [53] and solving for (2) results in
steady state error than ANN in response to required droop
deterministic model, as depicted in (3) [22]:
power suggested by swing equation. It is concluded that an
( )(
efficient droop response governed by swing equation requires
SAmb ( ))
a combination of an accurate inertia estimator based on ANN IL = NPAR IPHre f + 𝛼 iSC TCell − TRe f
and a robust nonlinear controller based on SM. Validation of Sn
proposed scheme is also established using a microgrid based ( )3 [ ][ 𝜀 𝜀g
] ( )
q g,re f VL +IL RS
TCell − −1
case study. −ISat ,n NPAR e k TRe f TCell
e nVT
TRe f
The remaining study is organized as follows: Section 2 out-
VL + IL RS
lines system description. Section 3 presents systematic ML − (3)
RSH
modelling to extract useful information from raw data, train
and improve models, and qualify suitable model for integration.
Section 4 presents results and discussion on control problem
2.2 Droop control and inertia emulation
and the significance of robust SM control solution aided by ML
technique. Section 5 presents conclusion and future work.
Microgrid power equilibrium is achieved by active and reactive
power controls, depending on frequency droop control and out-
put voltage control, respectively [54]. Active power required in
2 SYSTEM DESCRIPTION inductive microgrid bus is conventionally modelled as (4):
The system under consideration is consisted of 350 kW PVG EV sin 𝛼
operated under particular climate condition. System block dia- P = (4)
X
gram is presented in Figure 1. Control system is developed
for single source/load scenario. Climate input contains GHI where E, V , 𝛼, and X are inverter output voltage, bus nom-
and DBT information that drives 350 kW PVG as well as inal voltage, power angle and output reactance of inverter
ANN model for MPP prediction of the said PVG. Maximum respectively. This paper concentrates on active power control
power point tracking is achieved by a buck DC/DC converter only. Advantage of conventional droop control is its inde-
controlled by robust SM control scheme. SM controls the out- pendence from critical communication links between power
put power of buck converter based on swing equation and a sharing components, thus enabling high flexibility, modularity,
designated ROCOF profile. and redundancy. However, conventional droop control exhibits
poor transient response towards fast ROCOF events [54].
Additionally, conventional droop control is inadequate in PVG
2.1 Maximum power point estimation using because (4) lacks estimate about MPP [55]. Rapid active power
deterministic model control of PVG for frequency droop control is discussed in [9,
56] and modelled as (5):
Single diode equivalent circuit of PV cell is depicted in Figure 2.
( )
The output power of this PV cell is represented by (1). However, fg − f0
this is instantaneous power and is different from Pmax discussed Pout = PMPP (5)
f0 × DR %
in Section 2.2.
Pout is power added to the grid, PMPP is MPP estimate of PVG,
PL = IL × VL (1) fg is measured grid frequency, fo is nominal grid frequency
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4 KANWAL ET AL.

FIGURE 1 Block diagram of sliding mode-based droop control against designated ROCOF profile.

FIGURE 2 Equivalent circuit diagram of a PV cell.

and DR is the droop rate. Typical synchronous generators are

programmed at DR = 5 percent [57]. The 5 percent droop
rate implies that grid frequency variation of 2.5, Hz (for fo =
50Hz) summons 100% change in generator active power out-
put. Moreover, total frequency correction time of six-line cycles FIGURE 3 Power versus voltage graph of PVG illustrating concept of
(or 100 ms for fo = 60, Hz) is proposed in [58]. The most derated operation.
crucial component in (5) is PMPP that changes with operational
climate conditions of PVG. The lack of PMPP estimation results
in catastrophic grid operation wherein fg spirals out of dead- power of a particular generator (in our case PVG). In order to
band [5]. Recent publications such as [59–62] used another control a PVG by using (6), an estimate of PD and an exact
variant of swing equation i.e., measurement of f and df ∕dt are required simultaneously. On
the other hand, a PVG controlled by the swing equation in (5)
2HS df requires an estimate of PMPP and an exact measurement of f
PG = PD + (6)
f dt only, which implies a reduced number of sensors required for
control system implementation.
where PG , PD , H , S , f and df ∕dt are generated or source Figure 3 reveals ability to emulate variable power reserve, or
power, load power or power deficit, microgrid inertia, apparent inertia inside PVG. PVG at VLow or VHigh is capable of produc-
power, grid frequency and ROCOF respectively. The princi- ing similar power output that is P1 . However, operation at these
pal modelling difference between said works and our system points produces only fraction of PMPP . Consequently, PVG is
described in Section 2 is the utility of ANN to estimate base able to create power headroom that is equivalent to inertia in
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KANWAL ET AL. 5

power function P (t ) of continuous dummy variable t over the

interval [0, 1]. The quasi-sinusoidal pattern in Figure 6 repre-
sents fluctuations in MPP during a full day. The magnitude of
power is obviously greater during summer than the rest of the
seasons.

3.2 Pre-process data

Original dataset obtained in Section 3.1 contained outliers due

to sensor malfunction or weather station maintenance sched-
ules. The dataset is pre-processed to remove outliers. Moreover,
night-time GHI and DBT records are eliminated from final
FIGURE 4 Modelling workflow to solve ML problem [64].
dataset of 598 samples. The pre-processed dataset is formally
represented as:

conventional power generator. Power output is increased or FeatureData, D {GHI , DBT } ∈ ℝ598×2 .
decreased by bringing P1 near or far from PMPP . However, VHigh (7)
offers better converter efficiency and faster dynamic response ⃗ {Target MPP} ∈ ℝ598×1
Out put Data, O
due to sharper slope than VLow [63].

3.3 Derive features

3 MACHINE LEARNING BASED
MODELLING Objective of feature derivation or extraction is to eliminate
unnecessary predictors or features from dataset to reduce model
The workflow presented in this section systematically solves complexity. Dataset in (7) contains two features of GHI and
ML problem through various steps. The modelling outlined in DBT. Each feature is examined by Neighborhood Component
Figure 4 starts from acquisition of raw data, extracts crucial Analysis (NCA) to determine individual feature significance
data features, trains and iteratively improves models, and finally [65]. Non-zero feature score returned from NCA that is 11.99
integrates the best model in proposed application. The follow- for GHI and 18.67 for DBT. Thus, the fact that the two features
ing discussion summarizes the modelling workflow for robust are crucial for model integrity is validated.
droop control of 350kW PVG. There are a number of other features reported in literature
that influence MPP location on V-I curve e.g., relative humid-
ity, barometric pressure, diffuse horizontal irradiance (DHI)
3.1 Access data and aging etc. However, GHI and DBT features significantly
encompass the unmodeled dynamics as evident from following
3.1.1 Data description discussion.
Relative humidity is defined in [66] as the amount of water
This study aims to highlight potential of solar power generation vapor in the air expressed as the ratio between measured amount
in Pakistan. Geospatial map in Figure 5 presents the climate data of moisture and maximum amount of moisture. According
obtained from individual weather stations installed in 9 major to [67] that the magnitude of GHI is indirectly affected by
cities of Pakistan [46]. The climate data obtained from indi- an inversely proportional relationship between wind-speed and
vidual weather stations in each city is pre-processed to obtain relative humidity. Therefore, modelling a PVG with GHI effec-
long term average of daily peak irradiance and temperature tively accounts for the effect of relative humidity on MPP
values. location on the V–I curve as well.
This study uses the climate dataset of Islamabad in par- Barometric pressure is defined in [66] as the pressure or
ticular to train, validate and test algorithms. Weather station force per unit area exerted by the weight of atmosphere, as
in Islamabad is installed at National University of Science measured by a barometer. Fluctuations in barometric pressure
and Technology. GHI and DBT results are obtained from correlates with changes in atmospheric thickness, that eventu-
CMP21 pyranometer and CS215 temperature probe, respec- ally leads to systemic changes in the solar spectrum received on
tively. The collected weather data drives elementary load line the ground [68]. Therefore, modelling a PVG with GHI also
analysis on 350 kW PVG in Simulink, to obtain the respec- effectively accounts for the impact of barometric pressure on
tive MPP [22]. Original dataset contained 131,795 samples and MPP location as well.
represented in Andrew’s plot of Figure 6. Andrew’s plot is a Diffuse Horizontal Irradiance (DHI) is related to GHI by
tool used to represent multivariate data in two-dimensions to [66] as:
establish similarities among groups of data elements. Andrew
plot extrapolates each observation {x j , y j } into PVG maximum GHI = DNI × cos(z ) + DHI (8)
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6 KANWAL ET AL.

FIGURE 5 Long term average of daily recorded peaks of GHI and temperature in 9 major cities of Pakistan, period 2014–2017.

ALGORITHM 1 Gaussian Process Regression model training algorithm

1: Input Feature Data, D [GHI, DBT]

= {x1 , … xn } , where xi ∈ ℝ598×2
Output Data, O ⃗ {Target MPP}
= {y1 , … yn } , where yi ∈ ℝ598×1
2: Output GPR Model Y⃗
3: Select Kernel/Covariance function K (xi , x j |𝜃) as Non-isotropic
Rational Quadratic
4: For Loop i = 1 to n
Generate Latent variables f (xi ) ∼ GP (m(xi ), k(xi , x j )), where
m (xi ) = 0 is the mean
Estimate Basis function coefficients 𝛽i , noise variance 𝜎2 , and
hyperparameters 𝜃 of K (xi , x j |𝜃)
End For
5: Construct ⃖⃖⃗T 𝛽⃗ + ⃖⃖⃖⃗
Final GPR model as Y⃗ = h(x) f (x)
FIGURE 6 Andrew’s plot of multivariate climate data acquired from a 6: End
weather station in Islamabad, Pakistan.

where DNI is Diffuse Normal Irradiance (DNI) and z is the

solar zenith angle at the instance of measurement. As reflected sion problem. The models are individually trained using similar
from (8) modelling a PVG with GHI also effectively models the pre-processed dataset from (7). The following describes training
impact of DNI and DHI on MPP location on the V–I curve as process of each ML technique.
well.
Aging of PVG is a phenomenon which effectively dete-
riorates the PVG’s output power performance with time. 3.4.1 Gaussian process regression (GPR)
According to [69], a PVG’s power quality declines after reaching
at 80 percent of rated energy output level, that is, MPP defined Regression attempts to provide function that fits any given set
at STC. Factors like humidity and radiation result into corro- ⃗ Curve fit-
of observed data points (e.g. in this study D ∪ O).
sion, delamination, and cracking in PV panel surface. However, ting is non-linear regression technique that offers one such
these effects are considered long-term and are not reported to function to fit observed data points accurately. However, there
significantly degrade the accuracy of MPP estimate until after are infinite functions that can accurately fit given dataset.
25 years of service [70]. Since the presented work focuses on Firstly, infinite functions are assumed that have Multivari-
ultra-short term MPP forecasts only (spanning a few seconds), ate Normal (or Gaussian) Distribution [71]. This assumption
therefore aging is not expected to disturb model accuracy. is made without prior knowledge of training data. The infi-
nite functions are replaced with functions that accurately
fit available dataset, and this information is posterior. The
3.4 Model training current posterior is used as prior to obtain new posterior
with the arrival of future updates in dataset. Algorithm 1
This study uses two ML models of ANN and GPR to forecast presents sequential algorithm to develop GPR model to forecast
maximum output power of 350 kW PVG. This is a regres- MPP.
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KANWAL ET AL. 7

FIGURE 7 Typical architecture of a feed forward ANN.

3.4.2 Artificial neural network (ANN)

ANN is network or group of interconnected artificial neurons

that mimic biological neurons. ANN is consisted of input and
output layer of data processing units that are interconnected via FIGURE 8 Training performance of ANN algorithm to forecast MPP of
350 kW PVG. Inset presents error value of validation data subset after 1000th
one or more hidden neural layers. For instance, Figure 7 shows
epoch.
Feed Forward ANN architecture accepts input dataset D ⃗ input
data and after processing it through hidden layer of x neurons
generate output O. ⃗ Each element in D ⃗ is connected to input
neuron through weight matrix W; weighted inputs are added
by a bias (⃗b) to produce x-element net input vector N ⃗ . Finally,
⃗
vector N is transformed into output vector O. ⃗
ANN is ML procedure that depends on minimization of
loss function f . Algorithm 2 presents sequential algorithm
to calculate W and ⃗b for PVG output power forecast using
Levenberg-Marquardt (LM) technique for 350kW PVG output
power forecast [72]. LM assumes that loss function for particu-
lar problem is based on sum of square of errors. The algorithm
presented here calculates weights and biases of hidden layer
only. However, same algorithm with slight modification in
dimensions of W and ⃗b can be reused to obtain output layer
parameters as well. Moreover, algorithm divides original dataset
D into three subsets for training (70 percent), validation (15 per-
FIGURE 9 Error histogram with 20 bins.
cent) and testing (15 percent) purposes. Algorithm 2 uses similar
steps to model training dataset. However, model generalization
is controlled by validation subset only. Testing samples have ANN validation results are presented in Table 1. The val-
no effect on training and thus provide independent measure of idation check was concluded after epochs reached maximum
network performance during and after training. Description of limit. The impact of varying number of input training samples
validation is presented in Section 3.5. and number of hidden layer neurons is presented in Table 2.
Increasing the number of training samples in D and O ⃗ only has
very insignificant impact on final MSE score. However, increas-
3.5 Iterate models ing the number of neurons in the hidden layer improves MSE
score at the expense of training time. LM optimizer is compared
The next step in modelling is improvement of trained models. with Scaled-Conjugate Gradient (SCG) optimizer, whereby the
ANN and GPR after improvement are tested and compared former exhibited extremely good MSE score.
using MSE as primary performance metric. ANN algorithm Training performance converges very near to zero, as
simultaneously validates model output parameters along with presented in Figure 8.
training. Model validation is concluded if one of following Figure 9 presents error performance of ANN using error
conditions are satisfied. histogram with 20 bins. The errors exhibit gaussian like distri-
bution with most of the predicted samples in training, validation
1. Improvement iterations called Epochs reach maximum limit and test datasets having absolute error values in the vicinity of
as defined in Algorithm 2. −0.2478 W bin.
2. Damping factor 𝜇 exceeds maximum limit, that is, 𝜇max . GPR model improvement is consisted of two sub-steps.
3. Gradient of loss function drops below its minimum limit,
that is, ∇min , or, 1. K-fold cross validation,
4. Loss function ( fLoss ) becomes negative. 2. Hyper-parameter optimization.
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8 KANWAL ET AL.

ALGORITHM 2 ANN model training with Levenberg–Marquardt technique

1: Input Feature Data, D {GHI, DBT} ∈ ℝ598×2 .

⃗ {Target MPP} ∈ ℝ598×1
Output Data, O
Hidden layer parameters i.e.,
2: Output weight matrix, W ∈ ℝ2×n , and bias vector ⃗b ∈ ℝ1×n
where n = 10, are the number of neurons in hidden layer.?
D and O ⃗ into Training Data DR ∈ ℝm×2 , and O⃖⃖R⃗ ∈ ℝm×1 , where m = 418,

3: Split Validation Data DV ∈ ℝ 90×2 ⃖⃖⃗

, and OV ∈ ℝ 90×1 ,
Testing Data DT ∈ ℝ90×2 , and O ⃖⃖⃗
T ∈ℝ
90×1 .

4: Initialize 𝜇 = 10−3 𝜇inc = 10 Epochmax = 103 P⃖⃗

O = 0 (Initial Guess)
𝜇m = 1010 𝜇dec = 10−1 ∇min = 10−7 k = 0 (First Epoch)
5: Compute Error Vector, ⃗e = P⃖⃗ ⃖⃗ ⃖⃗ ⃖⃖⃗
T − PO : where PT ≡ OV ,
∑m
6: Compute Initial Loss function, fLoss_Old = ei 2 .
i=1
7: While Loop
𝜕ei
Compute Jacobian Matrix of Loss Function, Ji, j = , i = 1 … m and j = 1 … n.
𝜕w j

Compute Gradient Vector of Loss Function: ∇ fLoss = 2J T ⋅ ⃗e

Approximate Hessian Matrix of Loss Function: H ≈ J T ⋅ J + 𝜇I.
For Loop 1 l = 0 to n − 1
bl +1 = bl − H−1 J T ,
For Loop 2 g = 0 to 1 (Due to 2 features in DV )
Compute w(l +k+1,g) = w(l +k,g) − H−1 J T ⃗e
End For 1
End For 2
Output Power, P⃖⃗ ⃗
O = tansig (WDV + b ),

Compute ⃖⃗ ⃖⃗
Error Vector, ⃗e = PT − PO ,
∑m
Loss function, fLoss = ei 2 .
{ i=1
𝜇 − 𝜇dec , fLoss < fLoss_Old
Set 𝜇=
𝜇 + 𝜇inc , fLoss > fLoss_Old
Set k=k+1
Check If k⟨Epochmax ∨ 𝜇⟨𝜇max ∨ ∇ fLoss ⟩∇min ∨ fLoss ⟩0
True? Go to Step 7
False? Go to Step 8
End While
8 Check If fLoss < 0
True? Return W and ⃗b. Go to Step 9.
False? Return Error. Go to Step 9.
9 End

The dataset in (7) is divided into 5-sections or folds, where Residual plot in Figure 11b maps the error performance after
each fold is used to validate model performance at some point. optimization. The error values randomly concentrated along
Entire validation is completed in 5-steps, where at each itera- zero horizontal axis implies that the trained model describes the
tion only one -fold is used for validation, while rest of the folds data well.
are used for training. Figure 10 outlines five cross-validation Comparing the results in Tables 1 and 2 illustrates
iteration schemes. that the two models offer significantly accurate forecast
Automated hyper-parameter optimization feature of Statis- capability. It is observed that GPRMSE−V is greater than
tics and Machine Learning toolbox in MATLAB is used to ANNMSE−V , while the former trained and optimized way
select the best kernel function with minimum MSE response. slower than the latter. Therefore, ANN model is selected for
Optimization results are presented in Figure 11a and Table 3. integration.
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KANWAL ET AL. 9

FIGURE 10 Fivefold cross validation for GPR model improvement.

FIGURE 11 (a) Automated hyper-parameter optimization of GPR model. (b) Residual plot of GPR model.

TABLE 1 ANN model improvement results. ANN validation reduces the

loss function to a significantly low value after 1000 epochs or iterations

No. Parameter Symbol Value Unit

1. Improvement k 1000 –
iterations/epochs
2. Damping factor 𝜇 10 –
3. Gradient of loss function ∇ fLoss 368.42 –
4. Loss function fLoss 0.291 W
5. Training time – 3 s
6. Training MSE ANNMSE−R 0.08 W2
7. Validation MSE ANNMSE−V 0.116 W2
8. Testing MSE ANNMSE−T 0.398 W2

FIGURE 13 Schematic diagram of conventional hysteresis

function-based SM buck converter [78].

3.6 Integration

The most accurate model obtained from Section 3.5 that is

FIGURE 12 Trajectory S at a location within the vicinity of the sliding ANN is integrated in the robust droop control application of
manifold converges if the existence condition is satisfied [78].
this study.
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10 KANWAL ET AL.

TABLE 2 Impact of varying number of training samples and number of hidden layer neurons on MSE score of LM and SCG optimizer-based ANN
No. of No. of No. of No. of Training time (s) Validation MSE (W2 )
training validation testing neurons in
Test setup samples samples samples hidden layer SCG LM SCG LM

Too few training samples 180 209 209 5 1 3 1.14E+07 2.554

Optimum 418 90 90 5 1 3 8.18E+05 3.551
Too high training samples 538 30 30 5 1 3 5.56E+05 2.235
Too few training samples 180 209 209 10 1 5 6.07E+06 4.616
Optimum 418 90 90 10 1 3 2.98E+06 0.116
Too high training samples 538 30 30 10 1 4 1.03E+06 2.729
Too few training samples 180 209 209 20 1 7 1.22E+07 0.259
Optimum 418 90 90 20 1 8 3.54E+06 0.008
Too high training samples 538 30 30 20 1 6 5.50E+06 0.023

TABLE 3 GPR model improvement results of the state variables of the system as expressed in (10). U +
No. Parameter Symbol Value Unit and U − are either scalar values or scalar functions of x(t ), and
𝛼i denote the set of control parameters known as sliding coef-
1. Kernel function K (xi , x j |𝜃) Noninotropic rational –
quadratic
ficients and xi (t ) ∈ x(t ). Control law can be realized by Signum
function, as given by:
2. Training time – 385.2 s
{
3. Optimization – 30
1 i f S (x, t ) > 0
iterations
u (t ) = (10)
4. Validation MSE GPRMSE−V 131.81 W2 0 i f S (x, t ) ≤ 0

Physical implementation of (9) is limited by unbounded fre-

quency of operation, resulting in unwanted chattering effect [76,
4 CONTROL SYSTEM DESIGN 77]. The possible remedy of this problem is to use hysteresis
AND MODEL INTEGRATION function, as depicted in (11).
Buck DC/DC converter is switching non-linear system and lin-
⎧U + , i f S (x, t ) > Δ
ear control theory is insufficient to obtain precise and dynamic ⎪
output response [73]. SM control offers robustness and stabil- ⎪ −
ity against parameter uncertainties and is therefore motivating u(t ) = ⎨U , i f S (x, t ) < −Δ
choice of nonlinear control system design including Buck ⎪
⎪Previous State, Otherwise
converter [74]. SM enforces Buck converter dynamics to fol- ⎩
low desired or expected trajectory by continuously switching
between continuous structures as per internal state variables. ⎧U + , i f S (x, t ) > Δ
⎪
SM achieves this objective by coercing system to (a) hit the slid- ⎪
ing manifold, (b) stay on the sliding manifold, and (c) settle u(t ) = ⎨U − , i f S (x, t ) < −Δ (11)
on a stable equilibrium point. This section outlines general- ⎪
⎪Previous State, Otherwise
ized SM control law and later on presents a digital SM control ⎩
implementation for a Buck converter.
where Δ is an arbitrary number. This function provides delayed
change in state trajectory and therefore high frequency switch-
4.1 Generalized SM control design ing problem is resolved. The chattering of trajectory is now a
function of Δ. Sliding surface is mathematically expressed as
SM control law is a discontinuous function [75] and is expressed (12) [76]:
as:
{ ∑
m
U+ i f S (x, t ) > 0 S (x, t ) = 𝛼i xi (t ) (12)
u (t ) = (9) i=1
U− i f S (x, t ) < 0
Assuming that system is at initial state vector xi = x(t = 0)
where x(t ) is the state-variable vector, S (x, t ) is the instanta- and a trajectory Si = S (t = 0) located at some distance
neous feedback-tracking trajectory of the system and is function away from the sliding manifold. The necessary and sufficient
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KANWAL ET AL. 11

condition to satisfy the hitting condition is to design control law 4.3 System modelling
ui = u(t > 0) that transforms state variable into x(t > 0) and a
resultant trajectory S (t > 0) satisfying (13) [78]: System modelling of buck converter requires development
of its state-space description in terms of desired control
dS variables (voltage or current). Figure 13 presents schematic
S <0 (13)
dt diagram of second order PID Sliding Mode Voltage Con-
trolled (SMVC) buck converter. C , L, rL denote capacitor,
The inequality (13) is consequence of the Lyapunov second the- inductor, and instantaneous load resistance of buck converter,
orem on stability of which the Lyapunov candidate function respectively. iL , iC and iR represent the inductor, capacitor,
1
is V (S ) = S 2 . Compliance with (13) satisfies hitting con- and load currents, respectively. Vre f , vi and 𝛽vo represent
2
dition. After satisfying the hitting condition, next step is to reference, instantaneous input, instantaneous output voltages,
satisfy existence or sliding condition. According to this condi- respectively. 𝛽 is the feedback network ratio, while u is
tion, once trajectory S is within vicinity of sliding manifold, will either 0 or 1 representing switching state of SW (MOSFET
always be directed back to the sliding manifold, as depicted in switch).
Figure 12 The vicinity of the sliding manifold is represented by The states of choice for buck converter are illustrated in (15):
0 < |S | < 𝛿.
The existence condition can be fulfilled by inspecting the ⎡x1 ⎤ ⎡ Vre f − 𝛽vo ⎤ ⎡ Vre f − 𝛽vo ⎤
dS
local hitting condition S < 0 such that in the vicinity of 0 < ⎢ ⎥ ⎢ ⎥ ⎢ ⎥
dt
|S | < 𝛿 the following condition of (14) is satisfied [78]:
⇀
x = ⎢x2 ⎥ = ⎢ d (Vre f − 𝛽vo ) ⎥ = ⎢ 𝛽vo 𝛽 ( vo − vi u ) ⎥
⎢ ⎥ ⎢ dt ⎥ ⎢ rLC + ∫ dt ⎥
LC
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
dS dS ⎣x3 ⎦ ⎣∫ (Vre f − 𝛽vo )dt ⎦ ⎣ ∫ x1 dt ⎦
lim S ⋅ < 0 that can be rewritten as, ⇒ lim+ S ⋅ (15)
S →0 dt S →0 dt
where x1 , x2 , and x3 are voltage error, voltage error dynamics
dS
< 0 and limS →0− S ⋅ >0 (14) and integral of voltage error, respectively. After differentiation
dt of (15), state-space representation transforms into (16):

According to stability condition, the control action and the slid-

⎡ẋ 1 ⎤ ⎡0 1 0⎤ ⎡x1 ⎤ ⎡ 0 ⎤
ing coefficients must be so designed that during sliding phase, ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥
system trajectory settles on a stable equilibrium point O. As the ⎢ẋ 2 ⎥ = ⎢0 −1∕rLC 0⎥ ⎢x2 ⎥ + ⎢−𝛽vi ∕LC ⎥ u
state trajectory S moves along the sliding manifold, the invari- ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥
⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥
ance condition Ṡ = 0 ensures that the system will definitely ⎣ẋ 3 ⎦ ⎣1 0 0⎦ ⎣x3 ⎦ ⎣ 0 ⎦
settle on O [78].
⎡ 0 ⎤
⎢ ⎥ ⇀
4.2 SM control design for buck converter + ⎢𝛽vo∕LC ⎥ or, ẋ = A x + Bv + D (16)
⎢ ⎥
⎢ ⎥
The power electronic converter applications require to oper- ⎣ 0 ⎦
ate at constant switching frequency to minimize switching
losses. However, it is observed that hysteresis function-
based SM control switches converters at variable frequency 4.4 Controller design
in response to line or load variations. Moreover, hystere-
sis function introduces non-zero steady-state voltage error in SM controller design for Buck converter is summarized in two
converter output. Therefore, Pulse-Width Modulation (PWM) major steps [75]. The rest of this section expands on these
based SM control is adopted to keep switching frequency steps.
constant and maintain near zero steady-state voltage error,
simultaneously [75]. a. Design control law equation (vc ) using (12), (13) and (16),
PWM technique compares a desired control signal (vc ) with b. Design sliding coefficient ratios (𝛼i ).
ramp signal, and outcome is pulse or PWM signal with same
frequency as ramp signal. The fact that PWM signal has con- The sliding manifold based on state-space dynamics in (16) is
stant frequency provides opportunity to use it with the SM given by (17) [78]:
control law. SM control law can be used to manoeuvre vc to
drive a power electronic converter. However, this implementa- ⇀
S = 𝛼1 x1 + 𝛼2 x2 + 𝛼3 x3 = JT x (17)
tion requires establishing relationship between SM control and
duty cycle of PWM controller.
where JT = [ 𝛼1 𝛼2 𝛼3 ] represents sliding coefficients.
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12 KANWAL ET AL.

√𝛼
where 𝜔n = 3
, is the undamped natural frequency and
𝛼2
𝛼1
𝜁= √ , is the damping coefficient. The equations can be
𝛼2 𝛼3
rearranged as (23) [78]:

( )2
𝛼3 1 𝛼1
= 2 (23)
𝛼2 4𝜁 𝛼2

There are three types of linear second-order system responses,

underdamped (0 ≤ 𝜁 < 1), critically damped (𝜁 = 1), and over-
damped (𝜁 > 1). For this application, critically damped case is
FIGURE 14 Simulated static grid frequency event is programmed with a selected in which voltage error response is given by (24) [78]:
5% droop slope and 20 Hz/s ROCOF.
x1 (t ) = (A1 + A2t )e−𝜔n t (24)
Firstly, hitting condition for sliding manifold in (17) is
where A1 and A2 are determined by initial conditions. The time
expressed as (18) [78]:
constant for decay in response is depicted in (25):
⎧ Ṡ ⇀ √
= JT A x + JT BvS →0+ + JT D < 0 𝛼2
⎪ S →0+ 𝜏 =
1
= (25)
⎨ (18) 𝜔n 𝛼3
⎪ Ṡ T ⇀
⎩ S →0− = J A x + J BvS →0− + J D > 0
T T

Putting the values from (23) and 𝜁 = 1 in (25) to obtain (26):

Substituting from (16), and solving for vS →0+ = u = 1 and
vS →0− = u = 0 in (18) results into simplified existence condition 𝜏 =
2𝛼2
(26)
as (19): 𝛼1
( ) According to 1% criteria it is assumed that the settling time
∗ 𝛼1 1
0 < ueq = −𝛽L − iC (Ts ) is 5𝜏. Consequently, sliding coefficient ratios are presented
𝛼2 rLC
as:
𝛼3 ( )
+ LC Vre f − 𝛽vo + 𝛽vo < 𝛽vi (19) 𝛼1 𝛼
𝛼2 =
10 25
and 3 = 2 (27)
𝛼2 Ts 𝛼2 Ts
Selection of sliding coefficients JT must comply with existence
condition in (19), otherwise trajectory will not return to sliding The following section describes the design of coefficients in (27)
manifold. Translating ueq ∗ into instantaneous PWM duty cycle to design SM control law [78].
v
(d ) requires that 0 < d = c < 1. where vc and v̂ramp are con-
v̂ramp
trol voltage and ramp voltage respectively, and are illustrated as 4.5 Results and discussion
(20):
( ) This section presents inertia emulation for 350 kW PVG
𝛼1 1 𝛼 ( )
vc = ueq ∗ = −𝛽L − iC + LC 3 Vre f − 𝛽vo + 𝛽vo operated by a Buck DC/DC converter controlled by SM
𝛼2 rLC 𝛼2 control based derated constant voltage MPPT technique.
( ) Design objective of PVG SM control is to produce rapid droop
⇒ vc = −K p1 iC + K p2 Vre f − 𝛽vo + 𝛽vo, and v̂ramp = 𝛽vi response to simulated static and variable/dynamic ROCOF
(20)
event/s. The droop response is governed by (5), where PMPP
The next step in SM control design is selection of sliding coef-
is MPP estimate provided by ANN from Section 3.5. The
ficient ratios, that satisfy stability conditions. According to [79],
command voltage signal (vcmd ) is calculated based on droop
Ackerman formula is chosen for controller design. Solving (17)
response requirement from (5). It is also observed that upper
gives (21) [78]:
limit on vcmd is equal to PVG open circuit voltage (VOc ),
since input voltage (vi ) can never exceed it. Moreover, it is
d
S = 𝛼1 x1 + 𝛼2 x + 𝛼3 ∫ x1 dt = 0 (21) imperative that output droop power (Pout ) is directly dependent
dt 1
on the accuracy of maximum power the PVG can provide,
Rearranging (21) results into (22): that is, PMPP and this is the reason to opt the most accurate
and computationally light PV power estimation technique.
d2 d Table 4 presents the comparison of presented work with
2
x1 + 2𝜁𝜔n x1 + 𝜔n 2 x1 = 0. (22) contemporary or classical techniques employed in recent
dt dt
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KANWAL ET AL. 13

TABLE 4 Comparison of presented work with contemporary techniques used in existing literature for statistically assisted microgrid droop-based power control

Inertia
Test system/case estimation Converter
Ref. Year Problem study technique Power controller architecture Contribution

[80] 2022 Improve DC bus Standalone microgrid ANN Open loop ANN Boost and Droop based energy
voltage regulation with PV and battery based PWM Bidirectional management
and minimize grid storage system scheme for parallel
power mismatch microgrids acting as
load or source
alternately
[81] 2019 Inability of traditional Standalone microgrid – PI voltage and current Boost and Buck Experimental
droop control to supplied by PV and verification of
mitigate DC bus wind generators, parallel connection
voltage fluctuations loaded by resistive of multiple DC/DC
and constant power converters to
loads cooperatively
achieve droop
control in a
microgrid
[37] 2019 Automatic load Two area YSGA PID, fractional order Power inverter Performance analysis
frequency regulation interconnected PID, dual stage of YSGA optimized
of interconnected microgrid fractional order PID dual stage fractional
microgrid system containing wind one plus PI order PID to
penetrated by turbine, bio mitigate grid
renewable energy generator, micro frequency and
resources turbine and demand power excursions
response support
[33] 2019 Improve DC bus Microgrid containing ANN Droop integrator and Dual parallel Transient analysis of
voltage regulation PV arrays, fuel cells, ANN based duty connected buck DC microgrid to
and minimize grid EVs and battery cycle reference converters rapidly track
power mismatch storage generation different voltage
references in the
presence of load
disturbances
[35] 2021 Improve DC bus Two and three – Finite State Machine Boost converters First order observer
voltage regulation distributed based controller, design to overcome
and minimize grid generators-based droop gain model uncertainties
power mismatch microgrid cases controlled by cost or associated with
rating based power DC/DC converters.
sharing strategy Control law
eliminates output
voltage tracking
errors without
integrators
This 2023 Effectively and Utility grid interfaced ANN Swing-equation Buck converter Droop response
Work intelligently dispatch with a microgrid enforced by a droop governed by swing
a PVG in response baseload, PV and controller based on equation presented
to static and peaker generator ANN assisted as a combination of
dynamic ROCOF robust SM control an accurate inertia
events law estimator based on
ANN and a robust
nonlinear controller
based on SM

literature to solve statistically assisted microgrid droop-based (28) [78]:

power
( )
control. v 1000
vc = −0.629 × 106 iC + 98.8885 × 106 1 − o + v , and
SM control parameters are derived by using formulas pre- vcmd vcmd o
sented in Section 4.4., and are summarized in the Appendix, 1000
according to (5). The numeric values of sliding coefficients (K p1 v̂ramp = v (28)
vcmd i
and K p2 ) are plugged in (18) to obtain the final control law of
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14 KANWAL ET AL.

FIGURE 15 State trajectory of internal states of buck converter, in response to SM control operation against static ROCOF event.

FIGURE 16 Simulated dynamic grid frequency event with variable ROCOF starting at 0.1µs, and ranging between 43 and −23 Hz/s.

The results are computed for a GHI of 500 W/m2 , DBT of equilibrium. However, after fulfilment of droop response, states
25◦ C, and constant islanded load of 5 Ω. The system is simu- are restored at a stable equilibrium point of iC = −0.014A,
lated in Mathworks Simulink with a step size of 1¯s and a total Vre f − 𝛽vo = 0.62 V, and vo = 846.4 V.
simulation time of 1s.

4.5.2 Dynamic ROCOF droop response

4.5.1 Static ROCOF droop response
Droop response of the designed SM controller is evalu-
The static ROCOF event is programmed with a 5% droop slope ated using variable/dynamic ROCOF waveform presented in
and 20 Hz/s ROCOF, as presented in Figure 14. State tra- Figure 16. The state trajectory and time-series plots of indi-
jectory plot and time plots of individual states are presented vidual states are presented in Figure 17. After initially settling
in Figure 15. Initial states of the buck converter are settled at an equilibrium point of iC = −0.04 A, Vre f − 𝛽vo = 0.107 V,
at finite values, that is, iC = −0.04A, Vre f − 𝛽vo = 0.96 V, and and vo = 632.4 V, the dynamic ROCOF event generates state
vo = 632.5 V. The static ROCOF event perturbs the states from perturbation. However, after fulfilment of droop response the
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KANWAL ET AL. 15

FIGURE 17 State trajectory of internal states of buck converter, in response to SM control operation against dynamic ROCOF event.

FIGURE 18 Static droop response of PVG against 20 Hz/s ROCOF, using SM and multiple fixed gain PID variants (a) k p = 5, ki = 1, kd = 0, (b) k p = 5,
ki = 1, kd = 0.1, (c) k p = 10, ki = 10, kd = 0.1, (d) sliding mode.
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16 KANWAL ET AL.

FIGURE 19 Dynamic droop response of PVG against variable ROCOF, using (a) PID tuned at k p = 10, ki = 10, kd = 0.1 and (b) SM.

FIGURE 20 SM controller droop response against dynamic ROCOF event for (a) 500 W/m2 , 25◦ C, 5 Ω, (b) 750 W/m2 , 25◦ C, 5 Ω, (c) 1000 W/m2 , 25◦ C,
5 Ω, (d) 3 Ω, 1000 W/m2 , 25◦ C, (e) 5 Ω, 500 W/m2 , 25◦ C, (f) 7 Ω, 500 W/m2 , 25◦ C.

FIGURE 21 Internal states of buck converter against dynamic ROCOF event for (a) GHI variations of 500, 750 and 1000 W/m2 at 5 Ω load. (b) Load
variations of 3, 5, and 7 Ω at 500 W/m2 .
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KANWAL ET AL. 17

TABLE 5 Comparison of SM and multiple fixed gain PID variants for droop response against 20 Hz/s, 40 Hz/s and dynamic ROCOF, using controller
performance metrics

PID1 PID2 PID3 SM

kp = 5 kp = 5 kp = 10
ki = 1 ki = 1 ki = 10
Parameters Units kd = 0 kd = 0.1 kd = 0.1

ROCOF Hz∕s – – 20 40 Dynamic 20 40 Dynamic

Rise Time ms 75.34 75.36 75.361 75.365 NA 2 57.048 57.05 NA 6
Settling Time ms NaN1 118.9 130.306 130.306 NA 3 45.976 45.98 NA 7
Slew Rate W∕ms 675.35 675.2 675.153 675.114 NA 4 889.071 889.071 NA 8
Overshoot % 5.54 3.83 4.607 4.608 NA 5 0.116 0.117 NA 9
IAE W.s 5.48 × 103 5.33 × 103 4.89 × 103 5.67 × 103 4.1 × 103 0.8792 1.8018 510.9
ISE W2 2.24 × 108 2.34 × 108 2.23 × 108 2.57 × 108 2.9 × 107 8.02 × 103 4.19 × 104 4.53 × 105
ITAE W.s 0.006 0.005 0.005 0.005 2.5 × 103 8.79 × 10−7 1.8 × 10−6 260.9
ITSE W2 .s 223.67 234.42 223.27 256.75 1.9 × 107 0.008 0.042 2.31 × 105

1
Not a Number (NaN) due to undamped oscillations in output power.
2,3,4,5,6,7,8,9
Not Available (NA) due to multiple setpoints due to variable ROCOF event.

states are restored at a stable equilibrium point of iC = 2.13 mA, respectively. However, PID3 exhibited the best overall PID con-
Vre f − 𝛽 vo = 0.001 V, and vo = 632.6 V. trol performance. SM clearly outclassed PID3 in terms of faster
output rise time and settling time, greater slew-rate, smaller
overshoot, and better error metrics. The performance metrics
4.5.3 SM versus PID droop response are calculated for static droop response between simulation time
comparison [0.4, 1] s, where only one transition occurs.
The controller performance metrics are re-calculated to com-
SM performance is compared with multiple fixed gain Propor- pare robustness of SM with PID3 for fast ROCOF of 40 Hz/s.
tional Integral Derivative (PID) variants against several ROCOF SM performance deteriorates negligibly for a faster ROCOF, as
events and graphical results are presented in Figures 18 and 19 depicted in Table 5. Even though the normalized percentage
whereas Controller Performance Indicators (CPI) results are change in CPI for SM is much greater than PID3 , still SM out-
presented in Table 3. This study uses CPIs as Integral Absolute classes PID3 with far better performance metrics. The obvious
Error (IAE), Integral Square Error (ISE), Integral Time Abso- disadvantage of PID is the need to constantly retune controller
lute Error (ITAE), and Integral Time Square Error (ITSE) to gains with changing system dynamics. This disadvantage further
compare SM with PID. The formulas for CPI are depicted in exacerbates droop response during dynamic ROCOF event, as
(29), (30), (31), and (32) [82]: shown in Figure 19, where PID3 shows unabated oscillations.
∞
On the other hand, SM still outperforms PID3 with better CPI
IAE = |e (t )| dt (29) scores. The performance metrics are calculated for dynamic
∫0 droop response between simulation time [0.1, 1] s, where the
∞ entire dynamic ROCOF variation occurs.
ISE = e2 (t ) dt (30)
∫0
∞ 4.5.4 Impact of variable source and load
ITAE = t |e (t )| dt (31) variations on SM droop response
∫0
∞
SM based droop controller for PVG applications requires per-
ITSE = t e2 (t ) dt (32)
∫0 formance evaluation under variable climate or source, and
variable load conditions. Therefore, the SM droop controller is
PID gains are iteratively tuned to achieve better error perfor- subjected to multiple load and source variation scenarios against
mance. Oscillations in output power are depicted in Figure 18a the dynamic ROCOF event depicted in Figure 16. SM droop
against PID1 are due to lack of braking effect or zero deriva- response clearly follows the droop command (vcmd ) as per the
tive gain. Oscillations result in undefined settling time shown swing Equation (5) as depicted in Figure 20a,b,c,e. However,
in Table 5. Introducing a derivative gain significantly improves in case of 3 Ω and 7 Ω resistive loads in Figure 20d,f, the
settling time, as shown in Figure 18b,c against PID2 and PID3 SM controller initially reports errors particularly a huge value
 17521424, 0, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12739 by INASP/HINARI - PAKISTAN, Wiley Online Library on [26/04/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
18 KANWAL ET AL.

FIGURE 23 Block diagram of microgrid under study.

presented in Figure 22. The required droop response is the sim-

ulated dynamic droop response outlined in Figure 16 with a
minimum and maximum ROCOF of 43 and 23 Hz/s respec-
tively. Droop response is governed by (5) and commandeered
FIGURE 22 Comparison of impact of PVG inertia estimation accuracy by the SM control law in (26). In (5) PMPP represents estimated
on dynamic ROCOF response against GHI and DBT of 500 W/m2 and 25◦ C internal PVG inertia. PMPP estimation is done using already
respectively. (a) Deterministic, (b) GPR, (c) ANN.
established inaccurate deterministic model in (3) and more accu-
rate ANN and GPR models discussed in Section 3.5. PVG
in case of 3 Ω. These errors are attributed to damped oscil- under test is the 350 kW SunPower SPR-305E-WHT-D solar
lations in ic shown in Figure 21b, due to initial impedance module, simulated for GHI and DBT of 500 W/m2 and 25◦ C
mismatch between PVG and the resistive load. However, respectively.
SM based MPPT quickly realigns PVG source impedance It is observed that the ANN model in Figure 22c extracted
as reflected in asymptotically stable states in Figures 20d,f the most power during different ROCOF instances. GPR
and 21b. extracted the second-best power in Figure 22b, while the deter-
An interesting inference can be made in Figure 20a–c, that is, ministic technique in Figure 22a delivered the least amount of
the peak droop power amplitude increases with increasing GHI. power against the same climate conditions in overall simula-
This observation is in line with the expressions in Equations (3), tion. GPR and ANN exhibited at par superior performances,
(2) and (1)., whereby the increasing GHI (equivalent to SAmb ) as qualified in Section 3. Deterministic technique is prone to
boosts IPH , IL and in turn boosts PL in (2) as well. errors due to inherent inability to approximate PVG’s non-linear
behaviour.
It is also important to observe that in all the cases pre-
4.5.5 Accurate PVG inertia estimation sented in Figure 22, the SM control system exhibited robust
and robust droop control response toward ROCOF fluctuations and strictly followed
required droop power command from swing equation. This
The significance of an accurate inertia (or internal power implies that the most efficient droop response depends exclu-
reserve) estimation for a PVG to provide droop response is sively on the amalgamation of ANN with robust SM control.
 17521424, 0, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12739 by INASP/HINARI - PAKISTAN, Wiley Online Library on [26/04/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
KANWAL ET AL. 19

TABLE 6 List of components used in the presented case study with respective values

No. Name Title Type Value Unit Comment

1. DG1 PVG Source 350 kW ∙ Primary microgrid power source

∙ Rated at STC
∙ In simulation setup, this PVG produces PMPP of
49.71 kW at GHI and DBT of 170 W∕m2 and 25◦ C
2. DG2 Peaker generator Source 50 kW Secondary or emergency microgrid power source
3. Local load Base load Load 50 kW Rated baseload of islanded microgrid
4. Utility grid Source and load 5 MW 25 kV/50 Hz utility grid
5. Fault Phase to neutral short circuit at 1 s
6. Islanding relay Grid isolating contactor, operates at 1.7 s

A combination of ANN forecast with a linear controller (such It is evident from Figure 24c that the PVG’s consumed
as PID) to solve (5) is expected to create unabated oscilla- active power reserves exceeded the threshold of 90%, in both
tions in output power during dynamic ROCOF fluctuations, as the cases of ANN and deterministic forecasters. Consequently,
depicted in Figure 19a. Alternately a combination of determin- the saturation of PVG reserve triggered the secondary source
istic forecast with a non-linear controller (such as SM) to solve of power in the islanded microgrid, that is, peaker generator.
(5) prevents oscillations in output power, but instead under- Exact trigger times of each forecaster are shown in Figure 24b.
performs as depicted in Figure 22a. Therefore, it is imperative Time difference of Δt = 2.549 − 2.437 = 0.112 s, between the
to opt for a robust non-linear controller (SM) assisted by an two forecasters is evident. However, this subtle Δt has pro-
accurate inertia estimator algorithm (ANN). found impact on the actual fg nadir, as shown in Figure 24e.
Clearly, the ANN forecaster grasped the saturation of PVG ear-
lier than the deterministic forecaster, and issued an early trigger
4.5.6 Case study to peaker generator. Therefore, fg reached at a nadir of 48.8
Hz for ANN, in contrast with a nadir of 48.1 Hz for deter-
This section presents microgrid scenario, depicted in the block ministic forecaster. It is also shown that the swing equation-
diagram Figure 23 as a case study with individual compo- based droop response in Figure 24a ensured droop response
nents listed in Table 6 to further cement the validity of robustness.
proposed scheme. The presented scenario is inspired from
a multi-tier or multilayered grid frequency support mech-
anism whereby the PVG serves as primary power source, 5 CONCLUSION
as proposed in [83]. The microgrid scenario is simulated in
Simulink, for a duration of 10 s at a time-step or resolution A robust controller based on Sliding Mode (SM) control assisted
of 7.5 µs. A simulated phase to neutral fault occurs at 1 s by ML is presented for droop control and inertia estimation
and the microgrid is isolated (or islanded) from utility grid at of PV system interfaced autonomous microgrid. Algorithms
1.7 s. for Gaussian Process Regression (GPR) and Artificial Neural
In order to establish the importance of accurate MPP forecast Network (ANN) are presented and models are trained using
of PVG in response to ROCOF excursions, the PVG is deliber- historical climate data from Islamabad, Pakistan. Hyperparame-
ately operated at a GHI of 170 W/m3 . Operating at such a low ter optimization outcome of GPR model was compared with
GHI saturates the PVG against ROCOF disturbance, and trig- Levenberg-Marquardt based ANN model and mean square
gers the backup 50 kW peaker generator. Trigger threshold for error (MSE) was used as primary performance metric. ANN
PVG can be any finite numerical value; for instance, the trig- was declared frontrunner with the most accurate prediction
ger threshold in aforementioned simulation setup is selected result with validation MSE of 0.116 W2 and training time of 3 s.
as 90% of PMPP . A rapid trigger generation would overcome Subsequently the ANN forecaster was integrated in swing equa-
the active-power deficiency in the islanded microgrid and is tion to predict maximum power point of 350 kW PVG. The said
further expected to prevent unnecessary grid frequency fluctu- PVG was simulated against sharp static and dynamic ROCOF
ation from its nominal value of 50 Hz. However, a rapid trigger events; significance of SM based droop response was high-
requires an accurate estimate of instantaneous PMPP . The fol- lighted in comparison with PID based droop response under
lowing discussion compares the impact of an accurate and an multiple gain settings. Typical control system performance
inaccurate PMPP forecast mechanism, that is, ANN and deter- metrics were used to compare SM and PID, and observed
ministic inertia estimators respectively, over trigger timing and that SM delivered the finest performance overall. Finally,
eventually the grid frequency excursion. impact of accurate inertia estimation in terms of controller
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20 KANWAL ET AL.

FIGURE 24 Case study results for microgrid islanding operation. (a) Droop power required from swing equation and actual droop response due to SM control,
(b) active power generated by peaker generators, as instructed by ANN and deterministic techniques, (c) consumed active power reserve in percentage, due to ANN
and deterministic forecast simulations, (d) comparison of cumulative and individual active powers generated from PVG and peaker generator, (e) grid frequency
fluctuations due to ANN and deterministic technique’s intervention to trigger peaker generator, (f) ROCOF of ANN and deterministic grid frequency results.

performance was explored. Droop response with swing equa- The advent of ML algorithms has inspired to incorporate
tion governed by classical five parameter deterministic model biological inference systems in the mission critical fabric of
and ANN model was compared, and former returned con- microgrid management systems. Reinforcement learning is the
stant recurring steady state error. It is concluded that accurate recent example of such algorithms, that uses ML to mimic
reserve estimation with a robust control system exhibits excel- human decision making. However, such state-of-the-art tech-
lent performance for PVG based autonomous microgrid. The niques are still reliant on low-level accurate robust control
conclusion is further validated in the context of a microgrid case systems as presented here, to effectively dispatch a microgrid
study. in the foreseeable future.
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KANWAL ET AL. 21

NOMENCLATURE
iC Capacitive displacement current Ampere
RL(min) Minimum load resistance across Buck Ω
converter output
RL(max) Maximum load resistance across Buck Ω
Symbol Description Unit
converter output
PL Instantaneous PV output power Watt rL Instantaneous load resistance across Buck Ω
IL Instantaneous PV load current Ampere converter output
VL Instantaneous PV load voltage Volt 𝜏 Time constant for decay in response s
VOc Open circuit PV voltage Volt 𝜁 Damping coefficient
IPH Light generated current Ampere 𝛽 Feedback ratio
IPHre f Reference light generated current Ampere 𝜔n Control bandwidth rad∕s
NPAR Number of parallel PV strings – Ts Settling time ¯s
NSER Number of series PV modules – vi Buck converter input voltage Volt
SAmb Ambient irradiance Watt/m2 C Capacitance in buck converter ¯F
Sn Irradiance at 25◦ C Watt/m2 L Inductance in buck converter mH
𝛼 iSC Temperature coefficient of ISC %/◦ C fs Switching Frequency MHz
TCell Solar cell temperature ◦C K p1 Sliding Coefficient 1 H∕s
TRe f Reference temperature ◦C K p2 Sliding Coefficient 2 V∕V
ISat ,n Reference reverse saturation current pA
ISat Reverse saturation current Ampere
RS PV series resistance per module Ω
AUTHOR CONTRIBUTIONS
RSH PV shunt resistance per module Ω
Sidra Kanwal: Writing - review and editing; Muhammad Qasim
VT Thermal voltage Volt
Rauf: Writing - review and editing; Bilal Khan: Writing - review
q Charge on an electron Coulomb and editing. Geev Mokryani: Writing - review and editing
E Inverter output voltage Volt
V Nominal bus voltage Volt ACKNOWLEDGEMENTS
This work was supported in-part by Innovate UK GCRF
𝛼 Power angle Degree (◦ )
Energy Catalyst Pi-CREST project under Grant number 41358
X Inverter output reactance Ω
and in-part by British Academy GCRF COMPENSE project
n Diode ideality factor under Grant GCRFNGR3∖1541.
PMPP Maximum power point estimate of PVG at Sn KiloWatt
Pout PVG power added in the grid Watt CONFLICT OF INTEREST STATEMENT
The authors declare no conflicts of interest.
fg Measured grid frequency Hz
fo Nominal grid frequency Hz DATA AVAILABILITY STATEMENT
DR Droop rate Hz∕s The author has provided the required Data Availability State-
⃗
D Input data vector [Watt/m2 , ◦ C] ment, and if applicable, included functional and accurate links
W Weight matrix to said data therein.
⃗b Bias vector
ORCID
𝜇 Damping factor
Geev Mokryani https://orcid.org/0000-0002-6285-5819
k Improvement iterations or epochs
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24 KANWAL ET AL.

APPENDIX
Sliding mode controller design parameters, empirical formula
for calculation and nominal values used in simulation setup.

Empirical
Parameter Symbol formula Nominal Value Units Comments
Vre f 1000
Feedback ratio 𝛽 –
Vcmd vcmd
MPPT control signal vcmd [0, VOC ] V Desired output voltage
Open circuit voltage VOc 1000 V
Control bandwidth 𝜔n 3.14159 × 105 rad∕s
Settling time Ts 5∕𝜔n 15.9 ¯s
Input voltage vi [800, VOC ] V Limit defined at STC*
Capacitor C 1000 ¯F
Inductor L 300 mH
Switching frequency fs 5𝜔n ∕𝜋 0.5 MHz
Minimum load RL(min) 2 Ω 10% load
Maximum load RL(max) 20 Ω Full load
𝛼1
Sliding coefficient 1 K p1 ( ) 297402.6 H∕s = 0.629 × 106 Hz
𝛼1 1 𝛼2
𝛽L −
𝛼2 RL(min)C
𝛼3 𝛼3
Sliding coefficient 2 K p2 LC 29597315.4 V∕V = 98.8885 × 109
𝛼2 𝛼2

*STC are Standard Test Conditions i.e., GHI = 1000 W∕m2 and DBT = 25 ◦ C